A soccer ball of diameter 29 cm rolls without slipping at a linear speed of 3.6 m/s. Through how many revolutions has the soccer ball turned as it moves a linear distance of 18 m?
20 circumfrances
To find the number of revolutions the soccer ball has turned, we need to first calculate the circumference of the ball and then divide the linear distance traveled by this circumference.
The circumference of a sphere is given by the formula C = π * d, where C is the circumference and d is the diameter. The diameter of the soccer ball is 29 cm, so the circumference is:
C = π * 29 cm
Next, we need to convert the linear distance, 18 m, to centimeters (cm) since the circumference is in centimeters. There are 100 cm in 1 meter, so 18 m is equal to:
18 m * 100 cm/m = 1800 cm
Now that we have both the circumference and the linear distance in centimeters, we can calculate the number of revolutions:
Number of revolutions = (linear distance traveled) / (circumference)
Number of revolutions = 1800 cm / (π * 29 cm)
Number of revolutions ≈ 18.88
Therefore, the soccer ball has turned approximately 18.88 revolutions as it moves a linear distance of 18 m.